What other kind of AIs exist apart from goal-driven?
Whether all AI are goal-driven depends on how far you're willing to extend the definition of 'goal'.

AIs are often defined through their primary tasks. Face recognition is a process; a face recognition AI is a limited, special-purpose AI. Paperclip collection is a process, the Paperclip Maximizer is a general, goal-driven AI.

There will always be some sort of goal, but it may in certain cases become so nebulous it's really a stretch to continue calling it a goal. For example,  unsupervised learning (as suggested by Aiden Grossman) - the goal you set is "learn", with very little qualifiers. The underlying AI may develop in surprising and unexpected ways; it may even modify own goals.

Similarly, another "aimless" AI type is a simulator of biological intelligence - say, replicating neural connections of an insect in software, making it run and observing the behaviors. The AI itself is not given a specific goal - it's a tool/subject of study, not something directly producing results. Still, the goals are exactly the same as goals of the original insect: feed, multiply, stay safe; unattainable due to hardware limitations but still pursued.

Therefore, whether all AIs are goal-driven is arguable. The only AI that is not actually driven by any goal whatsoever is one that's switched off. But whether you consider all the possible nebulous, abstract or accidental goals that drive the AI to call it actually goal-driven, that's up to debate.